It’s getting tougher for U.S. savers to find a bank where they won’t end up paying to keep their money safe.

The average interest paid on savings, checking, money-market and certificate of deposit accounts fell to 0.99 percent in July, the first dip below 1 percent in a decade, according to researcher Market Rates Insight. Banks also have been raising fees and adding new ones, most recently in response to the financial-services overhaul bill that became law July 21.

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